I.  Original Lesson Plan

Lab 2: INSTRUCTIONAL TECHNOLOGY 

Lesson Plan Title: Adding Integers

Age Range:  Grade 5 through Grade 8 (Middle School)

Overview and Purpose: Students will use the story of “Hot and Cold Cubes” and two-color counters to develop the rules for adding positive and negative integers. This will help them visualize how numbers cancel each other out.

Objective: I can…
…add positive and negative integers together without using a visual aid.
…describe the general procedures for adding numbers of the same signs and different signs

Resources:
“Hot and Cold Cubes” story + (teacher created) worksheet
Two-color counters

Vocabulary

• Integer
• Neutral Pair
• Additive Inverse
• Positive number
• Negative number
• Positive/negative infinity

Instructional Activity
Activation:  
Remind students that we have spent the first three weeks of the summer program working with and thinking about fractions and how they relate to other numbers on the number line.  Draw a number line from 0 to positive infinity and then ask,  “What kind of numbers do we find if we go to the left of 0?”  

Mini-Lesson:
Review the definition of the word ‘integer’ (a positive or negative number or zero).   Review that the distance between each whole number on the number is equal so that the distance between 0 and 2 is the exact same as the distance between 0 and -2

Whole Class Activity

1. Give each group of students a fistful of counters and distribute the worksheets to each student. 
2. Have students read aloud the “Hot and Cold Cubes story
3. Check for understanding: Pause after paragraph TKTK
   • One hot cube is  +1 and cold cube is -1 
   • H + C = 0  (neutral pair)
4. Continue the read aloud.  
5. Students represent the problem, the chefs adding 4 hot cubes and 10 cold cubes 4 + (-10) = ___. 
6. Ask them to lay out four red counters to represent the positive number 4. They should then lay their ten yellow counters next to the four red. 
7. Q: Will the soup be colder or warmer than before all the cubes were added?
8. Q: What happens when we have a pair of one hot and one cold?  What will the 4 hot cubes do to all the ten cold cubes?  This shows that those pieces are canceled out. The one rice chex piece uncovered represents the answer of one.
9. Another problem on the board: -5 + 3 = ___. The students will lay out yellow and red colored counters to represent (-5) and +3 respectively.  The remaining two unpaired counters (-2).
10. Have students continue to work with you through guided practice until they understand how to represent hot and cold cubes as integers. Once they are comfortable with the skill, have them complete the worksheet. 

Closure:
Exit Ticket: Have students summarize the rules for adding integers

II. Revised Lesson Plan Using 5E Framework

The following are the components of the above lesson plan that were modified using the 5E framework.  All the components above the instructional activity would follow the same order.

Resources:
“Hot and Cold Cubes” (5E modified) story + (teacher created) worksheet|
Two-color counters
Laptops for each student

Instructional Activity

Engagement:  Draw a number line from 0 to positive infinity and then ask,  “What kind of numbers do we find if we go to the left of 0?”  Remind students that we have spent the first three weeks of the summer program working with and thinking about fractions and how they relate to other numbers on the number line.   We added, subtracted, multiplied and divided them and those results could also be placed on the number line.  Negative numbers, integers in this case, also exist on the number line and the results of adding, subtracting, multiplying and dividing them can also be placed on the number line.  How do they behave under these operations?

Exploration:  (Google Classroom) Students will read “Hot and Cold Cubes” (5E modified) with further modifications in their groups.  Groups may choose to read silently or aloud using group voice.  An unformatted version will be available in Google Classroom for students who need to translate the story or parts of it.  Checks for understanding and guiding questions will be integrated into the text (see highlighted parts in linked text) to help students discern the salient ideas of integer addition.  

Explanation:  Review the definition of the word ‘integer’ (a positive or negative number or zero).  Review that the distance between each whole number on the number is equal so that the distance between 0 and 2 is the exact same as the distance between 0 and -2.  Teacher will elicit and record any noticings from the first activity regarding the embedded guiding questions:  (1) Will the soup be colder or warmer than before all the cubes were added?  (2) What happens when we have a pair of one hot and one cold (i.e., a neutral pair)?  The aim here is to have students realize that the neutral pairs formed by adding quantities of opposite signs are subtracted away.  

Elaboration:  Students will complete the second activity.  Prior to starting the second activity students will have the opportunity to view selected videos that describe the adding of integers.  Questions 8 and 9 ask the students to generalize the method for solving scenarios where integers with the same signs are added and the scenario where they are adding integers with different signs.  Prior to the exit ticket, gather students in and ask a few to share their noticings and clarify any misconceptions.

Evaluation: (Google Forms) Exit tickets will be provided for students to answer the following questions:

1. What do you notice when you only add positive numbers (hot cubes)
2. What do you notice when you add positive and negative numbers (hot and cold cubes)  Are you adding? Why or why not?

III. Reflection

Some of the advantages of the 5E modified lesson is that it puts a greater emphasis on student collaboration and permitting each student to take a more active role in her learning.  The guiding questions in the text help students focus on the parts of the story that are relevant to the learning objectives.  This is especially useful for those students who may not be reading at grade level or have difficulty with comprehension.  A shorter version of the story at a lower lexile level can be offered either as a separate packet or in the Google Classroom lesson material to further differentiate for ELLs and SWDs.  I have not, however, undertaken this task as yet.  Although both lessons call for the use of manipulatives, the exploration and elaboration components allow the students more flexibility in how long they will use the manipulatives and other scaffolds to make sense of addition of integers and generalize an algorithm for addition of signed numbers.  These two components by allowing the teacher to work with each group also permits the teacher to offer very specific feedback.

One limitation to the 5E model is that it assumes that students are engaging the day’s content with a fair amount of prerequisite knowledge and are able to use these classroom experiences to build upon and deepen their understanding of a topic.  In my own experience, when there are significant deficits in student learning there needs to be more explicit instruction to optimize limited instructional time.  Another consideration in using the 5E model is for it to be really effective, teachers and students need to do a great deal of preparatory work to develop more mental dexterity (computational thinking strategies), greater comfort dealing with ambiguity within problems, more self-reflection regarding one’s learning and academic needs among other things.  Neither of these limitations are decisive blows to 5E or similar models.  In the first instance, teachers will need to find a balance between more explicit instruction and more independent student centered learning experiences that empower all students to meet the most important learning outcomes.  In the second instance, teachers need to be more deliberate about teaching and developing the problem solving strategies and mental aptitudes that will make 5E and the like effective and enjoyable.  

As for the technology that I recommended, I sought to keep it simple and stay in the Google suite.  If these instructional pivots are to become integral parts of one’s teaching repertoire going forward one needs to ensure that the planning and implementation is sustainable over the course of the school year.  I also have a bias towards maximizing the use of paper in pencil in the initial doing of math so my inclination when using technology is to facilitate multiple different opportunities to engage with the and for guided practice to help students gain greater facility with the subject matter.  In the latter instance, I would have students use IXL for independent practice.          

IV. Sources

CUNY EdTech. “Instructional design models: 5E.” Hostos .CUNY.edu. https://commons.hostos.cuny.edu/edtech/faculty/teaching-with-technology/instructional-design/5e/

Interactive Mathematics Program (IMP). “Hot and Cold Cubes.” Year One.

Singh, M. (2023). “5E instructional model: everything you need to know.”  Number Dyslexia. https://numberdyslexia.com/5e-instructional-model/